During the early part of the twentieth century, the drilling community did not account for the strengthening effect of downhole pressure on rock. I. G. Kühne, 1952, Die Wirkungsweise von Rotarymeiseln and anderen drehenden Gesteinsbohrern, Sonderdruck aus der Zeitschrift, Bohrtecknik-Brunnenbau, Helf 1-5, pointed out the effect of pressure and suggested that rock may be treated as a Mohr-Coulomb material. Research conducted at Rice University explored the ramifications of Kühne's proposal. R. O. Bredthauer, Strength Characteristics of Rock Samples Under Hydrostatic Pressure, Rice University Master's Thesis; R. A. Cunningham, The Effect of Hydrostatic Stress on the Drilling Rates of Rock Formations, 1955, Rice University Master's Thesis; E. M. Galle, 1959, Photoelastic Analysis of the Stress Near the Bottom of a Cylindrical Cavity Due to Non-Symmetrical Loading, Rice University Master's Thesis. Similar research spread rapidly through the industry.
This early research showed that the most important factor governing drillability downhole is the differential pressure, defined as the difference between the pressure of the mud in the borehole (borehole pressure) and the pressure in the pores of the rock (pore pressure). Differential pressure defines an effective stress confining the rock matrix and is much more important as an indicator of rock drillability than the tectonic stresses. These early researchers adopted a Mohr-Coulomb model in which differential pressure defines the hydrostatic component of stress. The drilling community still uses the parameters of a Mohr-Coulomb model, namely Unconfined Compressive Strength (UCS) and Friction Angle (N) to characterize rock. However, rates of penetration based on these models under-predict the effect of pressure on drilling, which suggests that there must be other rock properties that govern drilling under pressure.
Drilling data, reported as early as Cunningham's thesis referenced above, showed that differential pressure had a more profound effect on the rate of penetration than would be expected by the increase in strength of a Mohr-Coulomb material. It has also been proposed that there are other mechanisms at work which they described as various forms of a phenomenon called “chip hold down.” A. J. Garnier and N. H. Van Lingen, 1959, Phenomena Affecting Drilling Rates at Depth, Trans AIME 217; N. H. Van Lingen, 1961, Bottom Scavenging—A Major Factor Governing Penetration Rates at Depth, Journal of Petroleum Tech., Feb., pp. 187-196. Chip hold down refers to force that the drilling mud may exert on a cutting, or a bed of crushed material, due to differential pressure. The industry also recognized that permeability has a strong effect on differential pressure. R. A. Bobo and R. S. Hoch, 1957, Keys to Successful Competitive Drilling, Part 5b, World Oil, October, pp. 185-188. As a drill bit shears rock, the rock dilates, causing the pore volume to increase. If the rock is impermeable, this will cause a reduction of pore pressure, increasing differential pressure, strengthening the rock. More recent studies quantify these relationships. E. Detournay and C. P. Tan, 2002, Dependence of Drilling Specific Energy on Bottom-Hole Pressure in Shales, SPE/ISRM 78221, presented at the SPE/ISRM Rock Mechanics, Irving, Tex.; J. J. Kolle, 1995, Dynamic Confinement Effects on Fixed Cutter Drilling, Final Report, Gas Research Institute.
Complexities of the drilling process led some researchers to abandon confined strength measured in triaxial tests and define a “drilling strength” that can be determined empirically with a drill bit itself. R. A. Cunningham, 1978, An Empirical Approach for Relating Drilling Parameters, Journal of Petroleum Technology, July, pp. 987-991. While useful in predicting rates of penetration, such models give little insight into the physical process of rock destruction.
Another approach based on specific energy has also been used. R. Simon, 1963, Energy Balance in Rock Drilling, SPE Journal, December, pp. 298-306; R. Teale, 1964, The Concept of Specific Energy in Rock Drilling, Int. J. Rock Mech. Mining Sci. vol. 2, pp. 57-73. Specific energy is the energy required to remove a unit volume of rock and has the units n/m2 (psi). When drilling rock efficiently at atmospheric pressure, the specific energy approaches a number numerically close to the UCS of the rock. This is useful as a measure of the drilling efficiency. A driller can measure the specific energy of a drilling process, compare that to the UCS, and quantity how efficient the drilling process is.
It has been suggested that the foregoing concept could be applied to drilling under pressure. R. C. Pessier and M. J. Fear, 1992, Quantifying Common Drilling Problems with Mechanical Specific Energy and a Bit-Specific Coefficient of Sliding Friction, SPE 24584, presented at the 67th annual Technical Conference and Exhibition of the SPE, Washington. However, there remains the question of what strength should be used to define efficient drilling in the pressure environment. An obvious first guess might be that Confined Compressive Strength (CCS) defines the limit. However, the inventor herein has learned that plugging CCS determined by Mohr-Coulomb type relations into specific energy-based models of drilling under-predicts the increased difficulty of drilling at a given differential pressure. Recently, several papers have appeared exploiting specific energy methods in oil and gas drilling. F. E. Dupriest, 2005, Maximizing Drill Rates with Real-Time Surveillance of Mechanical Specific Energy, SPE 92194, presented at the SPE/IADC Conference. Amsterdam; H. Caicedo and B. Calhoun, 2005, SPE 92576, Unique ROP Predictor Using Bit-specific Coefficient of Sliding Friction and Mechanical Efficiency as a Function of Confined Compressive Strength, presented at the SPE/IADC Drilling Conference, Amsterdam; D. A. Curry and M. J. Fear, 2005, Technical Limit Specific Energy—An Index to Facilitate Drilling Performance Evaluation, presented at the SPE/IADC Drilling Conference, Amsterdam. Typically, these papers have laboratory-derived empirical relations defining a drilling strength, a number that is higher than the CCS.
In summary, the industry has realized for a long time that UCS and N are not sufficient to account for the increased difficulty of drilling with increasing hydrostatic pressure. However, these properties continue to be measured and quoted when describing rock.
Rates of penetration based on these models under-predict the effect of downhole pressure on drilling, which suggests that there must be other rock properties that govern drilling under pressure.